Given the function f(x) = −5x2 − x + 20, find f(3).

Answer:

angle CAD

Step-by-step explanation:

look at the 3 points that make up the angle

Assuming [tex]a[/tex] is a non-negative real number...

Raise both sides to the power 2 :

[tex]a^{3/4} = 8 \implies \left(a^{3/4}\right)^2 = 8^2 \implies a^{3/2} = 64[/tex]

which follows from the exponent product property, [tex](x^y)^z=x^{yz}[/tex]. In particular, 3/4 × 2 = 6/4 = 3/2.

Raise both sides to the power 1/3 :

[tex]\left(a^{3/2}\right)^{1/3} = 64^{1/3} \implies a^{1/2} = 4[/tex]

where we use the same property as before, and 4³ = 64. This time, 3/2 × 1/3 = 3/6 = 1/2.

Take the reciprocal of both sides. This negates the exponent, so we end up with

[tex]\dfrac1{a^{1/2}} = \dfrac14 \implies \boxed{a^{-1/2} = \dfrac14}[/tex]

Of course, you could also solve for [tex]a[/tex] immediately by raising both sides of the original equation to the power 4/3. We have 4/3 × 3/4 = 12/12 = 1, so

[tex]a^{3/4} = 8 \implies \left(a^{3/4}\right)^{4/3} = 8^{4/3} \implies a = 8^{4/3}[/tex]

Now 2³ = 8, so [tex]8^{4/3} = \left(8^{1/3}\right)^4 = 2^4 = 16[/tex], and since 4² = 16, it follows that

[tex]a = 16 \implies a^{1/2} = \sqrt{16} = 4 \implies a^{-1/2} = \dfrac14[/tex]

The sandbox can hold 48 cubic feet of sand in it if the sandbox with dimensions of 4 feet, 6 feet, and 2 feet.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape.

We have a sandbox:

The length of the sandbox = 4 feet

The width of the sandbox = 6 feet

The height of the sandbox = 2 feet

Amount of sand can hold = volume of the sandbox

= 4×6×2

= 48 cubic feet

Thus, the sandbox can hold 48 cubic feet of sand in it if the sandbox with dimensions of 4 feet, 6 feet, and 2 feet.

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Answer:

y - 10 = 2(x - 3)

Explanation:

Equation:

y - y₁ = m(x - x₁)

Here given:

coordinates: (x, y) = (3, 10)

Inserting value's:

y - 10 = 2(x - 3)  in point slope form

y = 2x - 6 + 10

y = 2x + 4  in slope-intercept form

Answer:

d) y - 10 = 2(x - 3)

Step-by-step explanation:

Given: a line with a slope of 2, and the point (3, 10)

⇒ Point-Slope Form: y - y₁ = m(x - x₁)

where: m is the slope, and (x₁, y₁) is a given point

Substitute the values into the form:

⇒ y - y₁ = m(x - x₁)

⇒ y - 10 = 2(x - 3)

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Answer:

1. -3(x+8) = -21
2. Division property of equality
3. x + 8 = 7
4. Subtraction Property of Equality

(Not quite sure whether #2 is division or distributive, but i'm 90% sure it's division).

The equation D = 1.5x/y represents the total distance traveled in km in terms of x.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

We have:

On the first journey, a cyclist traveled 1 1/2 km in x minutes.

As we know,

Speed = distance/time

Distance = 1 1/2 = 3/2 km = 1.5 km

time = x

Speed = 1.5/x

On the second journey, the same cyclist traveled for y hours at the same average speed as on his first journey.

Distance = speed×time

Distannce(D) = (1.5/x)(y)

D = 1.5x/y

Thus, the equation D = 1.5x/y represents the total distance traveled in km in terms of x.

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Answer:

y

Factor:4x^3-7x^2-30/y+15:

⬇

4x^3y-7x^2y+15y-30

y

Answer:

it takes 48 days for 15 men to work

it takes 16 days for 15/48*16

the answer is 5 men

Answer:

45 men

Step-by-step explanation:

If you 1/3 the amount of time (from 48 to 16 ) to weed the plot, you will need to TRIPLE the number of men    to     45  men

Answer:

[tex]\frac{42}{8}[/tex]

Step-by-step explanation:

7/8 <> 0.875

0.875 * 6 = 5.25

5.25 <> 42/8

(<> is used to show decimal to fraction and vice versa [the other way around])

Answer:

63

Step-by-step explanation:

180 - 117 = 63 which is used to figure out angle 2.

Angle 2 and angle 3 are corresponding angles thus the measure of angle 3 is 63 degrees.

Answer:

Search up online

Step-by-step explanation:

i don't actually know but searching online is good

The value of the variable x and y will be 1  2/3 and 4  2/3. Then the correct option is C.

The solution of the equation means the value of the unknown or variable.

The equations are given below.

y = 4x − 2  ...1

y = x + 3    ...2

Subtract equation 1 from 2, then we have

 0 = 3x – 5

3x = 5

 x = 5/3

 x = 1  2/3

Then the value of y will be

y = 5/3 + 3

y = 14 / 3

y = 4  2/3

Then the correct option is C.

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Answer:

19 months

Step-by-step explanation:

First off 682- 55 = 627. 627/33 = 19

Answer:

[tex]a=5 \sqrt{7}[/tex]

Step-by-step explanation:

Pythagoras Theorem explains the relationship between the three sides of a right triangle.  The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle:

    [tex]a^2+b^2=c^2[/tex]

where:

Given:

Substitute the given values into the formula and solve for a:

[tex]\begin{aligned}a^2+b^2 & = c^2 \\\implies a^2+9^2 & =16^2\\a^2+81 & =256\\a^2+81-81 & =256-81\\a^2 & =175\\\sqrt{a^2} & =\sqrt{175}\\a & =\sqrt{25 \cdot 7}\\& = \sqrt{25}\sqrt{7}\\& =5\sqrt{7}\end{aligned}[/tex]

Therefore, the measure of the third side of the given right triangle is [tex]5 \sqrt{7}[/tex]

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The answer is B

When there is a solid point that means it is included in the graph, so you'd use a greater/less than or equal to symbol (the one with a line under). If it's an unfilled point then it means that it is not included in the graph, so you'd use a greater/less than sign.

The x² equation is less than 2 while the linear equation is greater than or equal to 2.

We know it's the x² equation that is less than two because it has a curve in it.

Answer:

2x + 3.

Step-by-step explanation:

x + x + 3

= 2x + 3.

Answer:

2x+3

Step-by-step explanation:

x+x+3=2x+3

sum means to add both expression together and we can see there are 2 x's so we can add them and get 2x+3

Answer:

Step-by-step explanation:

0P=OA+AP

    =OA+2/5(AB)
    =(4,-5)+2/5(0,10)

    =(4,-5)+(0,4)

    =(4,-1)

therefore P(4,-1)

ANSWER AT THE BOTTOM

Question:

There is a bag with 1 red pen, 4 black pens, and 3 blue pens. If 2 pens are chosen from the bag without replacement, what is the probability that you chose 2 black pens.

Explanation:

Right now there are a total of 8 pens. 4 of them are black. So, the probability of choosing a black pen right now is 4/8, or 1/2.

Lets assume we picked a pen and got black.

Now there are only 7 pens in the bag, and only 3 of them are black. The probability of choosing a black pen right now is 3/7.

So on the first draw, the probability is 1/2

And on the second draw, the probability is 3/7

To find the probability of 2 ocurrences happening in a row, we must multiply their individual probabilities.

For example, if we wanted to find the probability of rolling two 6's in a row on a dice, we would need to mutiply the individual probability together. The probability of rolling one 6 is 1/6, so the probability of rolling two 6's in a row is 1/6 MULTIPLIED BY 1/6, which is 1/36.

The probability of rolling two 6's in a row is 1/36.

Lets apply the same principle to our situation right now.

So on the first draw, the probability is 1/2

And on the second draw, the probability is 3/7

1/2 MULTIPLIED BY 3/7    =    3/14

3/14 in decimal form is 0.21

ANSWER:

0.21, OR 21%

The graph of (2x - 1) / (x + 2) have intercepts at (0.5, 0) and (0, -0.5), The graph of (1 - 4x) / (1 - x) have intercepts at (0, 1) and (0.25, 0) and The graph of (-3x - 4) / (x + 2) have intercepts at (-1.33, 0) and (0, -2).

An equation is an expression that shows the relationship between two or more numbers and variables.

Plotting the graph using geogebra online graphing tool.

The graph of (2x - 1) / (x + 2) have intercepts at (0.5, 0) and (0, -0.5), The graph of (1 - 4x) / (1 - x) have intercepts at (0, 1) and (0.25, 0) and The graph of (-3x - 4) / (x + 2) have intercepts at (-1.33, 0) and (0, -2).

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Answer:

A.) 588329.896

B.) 274300

C.) 1657.18474

D.) 1.002

(All answers unrounded.)

Explanation:

I converted each unit to the unit used in the other number (E.g., for question A I converted tons to kilograms, and then finished solving.)

Answer:

f(x)=5000(1+0.05)^x

Step-by-step explanation:

Use the formula: f(x)=P(1+b)^x

P is principal or y-intercept. 5000 is principal.

b is the percentage in decimal form. 0.05 is b.

x is time, in this case years. Since there is not a certain number of years leave x as x.

f(x)=5000(1+0.05)^x

Hope this helps!

If not, I am sorry.

Therefore, [tex]\frac{8}{7}= 1.14[/tex] cannot represent the probability of an event. So, option C is correct.

We need to identify which of the given option cannot represent the probability of an event.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.

By simply dividing the favourable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favourable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

Now, [tex]\frac{1}{14} =0.0714, \frac{8}{7}= 1.14[/tex] and [tex]\frac{20}{21}=0.952[/tex].

Therefore, [tex]\frac{8}{7}= 1.14[/tex] cannot represent the probability of an event. So, option C is correct.

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The denominator of the simplified expression will be (9n² + 4).

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The expression is given below.

[(2 / 6n + 4)] [(3n + 2) / (3n – 2)]

On multiplication, we have

(6n + 4) / (18n² + 8)

(3n + 2) / (9n² + 4)

The denominator of the simplified expression will be (9n² + 4).

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Answer:

y=2x+1

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

In triangle JKL, the side opposite the 30 degree angle, JL, is half the length of the hypotenuse, KL. Thus, JL has a length of

[tex]4 \sqrt{2} [/tex]

In triangle JML, the hypotenuse is

[tex] \sqrt{2} [/tex]

times the length of the leg, meaning that x = 4

Answer:

y=⅓x+b

Step-by-step explanation:

So basically the formula of slope-intercept is:

y=mx+b

and m=⅓

so

y=⅓x+b and it includes the point (0, 6) so:

6=⅓(0)+b===> b=6===> y=⅓x+6

Answer:

Just think of which number, when you multiply it with 20 will give you -8

and then you multiply that number with -4 to get y. Hope it helps!

Using the relation between velocity, distance and time, it is found that t = 3 hours.

Velocity is distance divided by time, hence:

[tex]v = \frac{d}{t}[/tex]

For this problem, the parameters are given as follows:

d = 15 miles, v = 5 mph

Hence the time in hours is found as follows:

[tex]v = \frac{d}{t}[/tex]

[tex]5 = \frac{15}{t}[/tex]

5t = 15

t = 15/5

t = 3 hours.

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If 30 is half price, then what is full price?

You can set up this problem like this:

30 = x/2

OR

30 = (1/2)x

where x is the full price.

To solve, simply multiply each half by 2:

2(30) = 2((1/2)x)

x = $60

Answer:

69 degrees

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

<1 = 39+ 30

<1 = 69